Hello, I asked help for this problem several times to no answer. I dont understand it and can use any help. Please, and thank you. please see the picture attached!

Answer:

The tower deviates [tex]64^\circ36'[/tex] from the vertical.

Step-by-step explanation:

Having 3 point of our new plane we can construct vectors on the plane by substacting 2 of them:

[tex]v_1=(0,3,2)-(0,0,0)\\v_2=(1,3,0)-(0,0,0)[/tex]

These vectors are on the plane, so a cross product between them will give us a vector perpendicular to the plane:

[tex](0,3,2)\times(1,3,0)=\left[\begin{array}{ccc}i&j&k\\0&3&2\\1&3&0\end{array}\right] =(-6,2,-3)[/tex]

Asuming that the aliens used our conventions, the original plane was perpendicular to the z axis, so that a perpendicular vector to that plane was

(0,0,1)

We know that a dot product between 2 vectors |V.W| = |V| |W| cos(α), where α is the angle between them. If we use the vector perpendicular to this plane, and the one perpendicular to the original plane, α will represent the deviation angle of our new plane.

[tex]\|(-6,2,-3)\|=7\\\|(0,0,1)\|=1[/tex]

[tex](-6,2,-3)\odot(0,0,1)= 7 cos(\alpha )\\\\ -3=7 cos(\alpha ) \\ \alpha=arc\ cos \frac{-3}{7} =115.37 ^\circ\\[/tex]

Since this angle is greater than 90 degrees it means that the vector we calculated as perpendicular to the plane points towards negative z (this can be seen by the -3 z component)

To fix this we can calculate a new perpendicular vector, or simply compare ir with the vector (0,0,-1). The latter is easier:

[tex](-6,2,-3)\odot(0,0,-1)= 7 cos(\alpha )\\\\ 3=7 cos(\alpha ) \\ \alpha=arc\ cos \frac{3}{7} =64.6^\circ =64^\circ36'[/tex]

Answer: There are 1,816,214,400 ways for arrangements.

Step-by-step explanation:

Since we have given that

"REPRESENTATION"

Here, number of letters = 14

There are 2 R's, 3 E's, 2 T's, 2 N's

So, number of permutations would be

[tex]\dfrac{14!}{2!\times 3!\times 2!\times 2!}\\\\=1,816,214,400[/tex]

Hence, there are 1,816,214,400 ways for arrangements.

Step-by-step explanation:

To prove it we just use the definition of similar matrices and properties of determinants:

If [tex] A,B[/tex] are similar matrices, then there is an invertible matrix [tex]C[/tex], such that [tex] A=C^{-1}BC}[/tex] (that's the definition of matrices being similar). And so we compute the determinant of such matrix to get:

[tex]det(A)=det(C^{-1}BC)=det(C^{-1})det(B)det(C)[/tex]

[tex]=\frac{1}{det(C)}det(B)det(C)=det(B)[/tex]

(Determinant of a product of matrices is the product of their determinants, and the determinant of [tex]C^{-1}[/tex] is just [tex]\frac{1}{det(C)}[/tex])

Answer:

C. Probability is 0.90, which is inconsistent with the Empirical Rule.

Step-by-step explanation:

We have been given that on average, the parts from a supplier have a mean of 97.5 inches and a standard deviation of 6.1 inches.

First of all, we will find z-score corresponding to 87.5 and 107.5 respectively as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{87.5-97.5}{6.1}[/tex]

[tex]z=\frac{-10}{6.1}[/tex]

[tex]z=-1.6393[/tex]

[tex]z\approx-1.64[/tex]

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{107.5-97.5}{6.1}[/tex]

[tex]z=\frac{10}{6.1}[/tex]

[tex]z=1.6393[/tex]

[tex]z\approx 1.64[/tex]

Now, we need to find the probability [tex]P(-1.64<z<1.64)[/tex].

Using property [tex]P(a<z<b)=P(z<b)-P(z<a)[/tex], we will get:

[tex]P(-1.64<z<1.64)=P(z<1.64)-P(z<-1.64)[/tex]

From normal distribution table, we will get:

[tex]P(-1.64<z<1.64)=0.94950-0.05050 [/tex]

[tex]P(-1.64<z<1.64)=0.899[/tex]

[tex]P(-1.64<z<1.64)\approx 0.90[/tex]

Since the probability is 0.90, which is inconsistent with the Empirical Rule, therefore, option C is the correct choice.

Answer: P(3) is True

Step-by-step explanation:

The given statement is an inequality denoted as P(x). To find out which of the options is true you have to evaluate each given value of X in the inequality and perform the arithmetic operations, then you have to see if the expression makes sense.

For P(0): Replace X=0 in 2x+5>10

2(0)+5>10

0+5>10

5>10 is false because 5 is not greater than 10

For P(3): Replace X=3 in 2x+5>10

2(3)+5>10

6+5>10

11>10 is true because 11 is greater than 10

For P(2): Replace X=2 in 2x+5>10

2(2)+5>10

4+5>10

9>10 is false

For P(1): Replace X=1 in 2x+5>10

2(1)+5>10

2+5>10

7>10 is false

Answer: The purchase price of the property is $112,500.

Step-by-step explanation:

Let the original value of property be 'x'.

Discount rate = 3%

Amount of discount = $2700

According to question, it becomes,

[tex]\dfrac{3}{100}\times x=2700\\\\x=\dfrac{2700\times 100}{3}\\\\x=\$90000[/tex]

Rate of down payment = 20%

So, Remaining rate of payment = 100-20 = 80%

So, Purchase price of the property would be

[tex]\dfrac{80}{100}\times x= 90000\\\\0.8\times x=90000\\\\x=\dfrac{90000}{0.8}\\\\x=\$112,500[/tex]

Hence, the purchase price of the property is $112,500.

Answer:

[tex]12.0\%=0.12[/tex]

Step-by-step explanation:

We have been given that your friend borrows $100 from you and promises to pay you back $109 in 8 months.

We will use simple interest formula to solve our given problem.

[tex]A=P(1+rt)[/tex], where,

A = Amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

Convert 8 months to year:

[tex]\frac{8}{12}\text{ year}=\frac{2}{3}\text{ year}[/tex]

[tex]108=100(1+r*\frac{2}{3})[/tex]

[tex]108=100+r*\frac{2}{3}\times 100[/tex]

[tex]108-100+r*\frac{200}{3}[/tex]

[tex]108-100=100-100+r*\frac{200}{3}[/tex]

[tex]8=r*\frac{200}{3}[/tex]

[tex]8\times \frac{3}{200}=r*\frac{200}{3}\times \frac{3}{200}[/tex]

[tex]\frac{24}{200}=r[/tex]

[tex]r=\frac{24}{200}[/tex]

[tex]r=0.12[/tex]

Convert to percent:

[tex]0.12\times 100\%=12\%[/tex]

Therefore, you are charging 12% APR to you friend.

Answer:

No , any two quadrilaterals may not be similar if  their corresponding angles are congruent.

Step-by-step explanation:

We need to check that whether two quadrilaterals are similar if

their corresponding angles are congruent.

A  quadrilateral is a polygon having two sides .

Two figures are said to be similar if they have same shape .

Two angles are said to be congruent if they have same measure .

Consider two quadrilaterals :  rectangle and square

Each angle of square and rectangle is equal to [tex]90^{\circ}[/tex] . So, their corresponding angles are congruent .

But square and rectangle are not similar as they have different shape .

Answer:

35

Step-by-step explanation:

Given that A,B, C are three non empty sets.

[tex]n(A) =n(B) =n(C) =17\\n(A \bigcap C) = 7\\n(A \bigcap B) = 5\\n(B \bigcap C) = 6\\n(A \bigcap B \bigcap C) = 7[/tex]

Use the addition theory for finding no of elements in union of two or more sets

We have addition theorem as

[tex]n(AUBUC) = n(A)+n(B)+n(C)-n(A \bigcap B)-n(B  \bigcap C)-n(A  \bigcap C)+n(A  \bigcap B \bigcap C)[/tex]

Now substitute for each entry from the given information

[tex]n(AUBUC) = 17+17+17-5-6-7+2\\= 53-18\\=35[/tex]

Answer:

Step-by-step explanation:

Since your population are the students in math class, you can use the z-score formula [tex]z=(x-\mu)/\sigma[/tex] in order to comparing the two math test scores. Where [tex]\mu [/tex] is the mean for the class, [tex]\sigma [/tex] is the standars deviation and x is Mary score.

For the first test [tex]\mu=.71 , \sigma=.18,x=.87[/tex] , so ,[tex]z_{1} = (.87-.71)/(.18)=.88[/tex].

For the second test [tex]\mu=.53 , \sigma=.14,x=.66[/tex] , so ,[tex]z_{1} = (.66-.53)/(.14)=.93[/tex]

Mary do better in the second test, relative to the rest of the class (because  [tex].88 \leq .93[/tex], it means the second score is nearer to the mean score of the class than the first one )  

The particular solution to the differential equation with the initial condition P(0) = 3000 is given by P = 3000e^((ln(2)/6)t), where P represents the population at time t. The growth rate is proportional to the population, and the constant of proportionality is ln(2)/6. This equation can be derived by solving the differential equation and using the initial condition.

In this problem, we are given that the population of a suburb grows at a rate proportional to the population. We are also given that the population doubles in size from 3000 to 6000 in a 6-month period. We need to find the particular solution to the differential equation with the initial condition P(0)=3000.

Let's denote the population at time t as P(t). Since the growth rate is proportional to the population, we can write the differential equation as dP/dt = kP, where k is the proportionality constant.

Integrating both sides of the equation, we get: ∫dP/P = ∫kdt. This gives us ln|P| = kt + C, where C is the constant of integration.

Using the initial condition P(0) = 3000, we can substitute t = 0 and P = 3000 into the equation to get: ln|3000| = 0 + C. Solving for C, we find C = ln|3000|.

Substituting C = ln|3000| back into the equation, we have ln|P| = kt + ln|3000|. Simplifying, we get ln|P| - ln|3000| = kt.

Since ln|P| - ln|3000| = ln|(P/3000)|, we can write the equation as ln|(P/3000)| = kt.

Taking the exponential of both sides, we get |(P/3000)| = e^(kt).

Since the population cannot be negative, we can remove the absolute value sign and write the equation as (P/3000) = e^(kt).

Substituting the doubling in size from 3000 to 6000 in a 6-month period, we have (6000/3000) = e^(k(6)).

Simplifying, we get 2 = e^(6k).

Taking the natural logarithm of both sides, we have ln(2) = ln(e^(6k)).

Using the property ln(a^b) = bln(a), we can rewrite the equation as ln(2) = 6kln(e).

Since ln(e) = 1, we have ln(2) = 6k.

Solving for k, we get k = ln(2)/6.

Substituting k = ln(2)/6 back into the equation, we have (P/3000) = e^((ln(2)/6)t).

Multiplying both sides by 3000, we get P = 3000e^((ln(2)/6)t).

This is the particular solution to the differential equation with the initial condition P(0) = 3000.

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Answer:

equilibrium point (10,340)

Step-by-step explanation:

To find the equilibrium point, equal the demand and the supply:

[tex]D(q)=S(q)\\\\-6.10q^2-5q+1000=3.2q^2+10q-80[/tex]

Reorganize the terms in one side and reduce similar terms:

[tex]3.2q^2+6.1q^2+5q+10q-80-1000=0\\\\9.3q^2+15q-1080=0[/tex]

that's a cuadratic equation, solve with the general formula when:

a=9.3, b=15, c=-1080

[tex]q_{1}=\frac{-b+\sqrt{b^{2}-4ac} }{2a}\\\\q_{2}=\frac{-b-\sqrt{b^{2}-4ac} }{2a}\\\\q_{1}=\frac{-15+\sqrt{(-15)^{2}-4(9.3)(-1080)} }{2(9.3)}\\\\q_{1}=\frac{-15+201}{18.6}\\\\q_{1}=\frac{186}{18.6}\\\\q_1=10[/tex]

q can't be negative because it is the quantity of bike frames, so:

[tex]q_{2}=\frac{-b-\sqrt{b^{2}-4ac} }{2a}\\\\q_{2}=\frac{-15-\sqrt{(-15)^{2}-4(9.3)(-1080)} }{2(9.3)}\\\\q_{2}=\frac{-15-201}{18.6}\\\\q_{2}=\frac{-216}{18.6}\\\\[/tex]

This value of q can't be considered.

Then substitute the value of q in D(q) to find the price p:

[tex]D(10) = -6.10(10)^2-5(10) + 1000\\\\D(10)=340=p[/tex]

The equilibrium point (q,p) is (10,340).

To find the equilibrium point in supply and demand equations, calculate where the two equations intersect to determine the equilibrium quantity and price.

Equilibrium Point Calculation:

Answer:

[tex]y(x)=x^2+5x[/tex]

Step-by-step explanation:

Given: [tex]y'=\sqrt{4y+25}[/tex]

Initial value: y(1)=6

Let [tex]y'=\dfrac{dy}{dx}[/tex]

[tex]\dfrac{dy}{dx}=\sqrt{4y+25}[/tex]

Variable separable

[tex]\dfrac{dy}{\sqrt{4y+25}}=dx[/tex]

Integrate both sides

[tex]\int \dfrac{dy}{\sqrt{4y+25}}=\int dx[/tex]

[tex]\sqrt{4y+25}=2x+C[/tex]

Initial condition, y(1)=6

[tex]\sqrt{4\cdot 6+25}=2\cdot 1+C[/tex]

[tex]C=5[/tex]

Put C into equation

Solution:

[tex]\sqrt{4y+25}=2x+5[/tex]

or

[tex]4y+25=(2x+5)^2[/tex]

[tex]y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}[/tex]

[tex]y(x)=x^2+5x[/tex]

Hence, The solution is [tex]y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}[/tex] or [tex]y(x)=x^2+5x[/tex]

Answer:

the primes are all the even numbers in the equation

Step-by-step explanation:

Answer:

If you purchase it, you are going to save 0.43 = 43% of the original price

Step-by-step explanation:

This problem can be solved by a rule of three.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

In this problem, we have the following measures:

-The prices

-The percentage that the price represents.

As the value of one measure increases, so do the value of the other. It means that we have a direct rule of three.

The problem states that the model you really like happens to be on sale for $400. It's original price is $700.

You saved $700-$400 = $300.

What percent of the original price will you save if you purchase it?

How much is $300 of $700.

$700 - 1

$300 - x

700x = 300

[tex]x = \frac{300}{700}[/tex]

[tex]x = 0.43[/tex]

If you purchase it, you are going to save 0.43 = 43% of the original price

Answer:

1 light-minute ≈ 1.12×10⁷ miles, three significant figures.

Step-by-step explanation:

Light-second is equal to the distance traveled per second by light in space, which is equal to 299,792,458 metres. Other units used are light-day, light-hour and light-minute.

Significant figures are the figures or digits of a number that carry meaning and contribute to the precision of the given number.

1 light-minute = 1.118×10⁷ miles, has four significant figures.

To express this number in three significant figures, the given number is rounded.

1 light-minute = 1.118×10⁷ miles ≈ 1.12×10⁷ miles, has three significant figures, as the non-zero digits are significant.

Answer:

  67.73625

Step-by-step explanation:

The dot (scalar) product is also the sum of products of corresponding vector components.

~a • ~b = 9·2.97 +6.75·6.075 +0·0 = 27.73 +41.00625 = 67.73625

The scalar product or dot product of two vectors, ~a and ~b, in Cartesian form is calculated by multiplying the matching components of the two vectors and then adding them. Performing these steps will give us 67.73625, which represents the magnitude of ~a with the magnitude of the projection of ~b onto the direction of ~a.

In physics, the scalar product, also known as dot product, of two vectors like ~a = h9, 6.75, 0i and ~b = h2.97, 6.075, 0i can be determined using their magnitudes and the cosine of the angle between them. However, in the given question, the vectors are in Cartesian form (i,j,k coordinate system), and we can calculate their dot product directly. The dot product is calculated by multiplying the respective i, j, and k components of the two vectors and then adding them. Let's do this step by step:

This scalar product gives the product of the magnitude of ~a with the magnitude of the projection of ~b onto the direction of ~a.

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Answer:

The 5.5 would be called a parameter.

Step-by-step explanation:

A parameter in statistics is a data/number/quantity that gives you information about an entire population. Given that Dr. Johnson asked ALL of her students to respond the question and the median of 5.5 was based on ALL of her students, we can say that this number would be a parameter for the population (in this case, Dr. Johnson's class)

Step-by-step explanation:

First:

(Error/Total )x 100%

(0.49/23) x100%= 2.13%

Second:

(Absolute uncertainty/mean) x100%

(3/44)x100%= 6.81%

To calculate percent uncertainty, divide the uncertainty by the measured value and multiply by 100%. The percent uncertainty for the measuring tape is 0.0213%. The percent uncertainty for heartbeats (converted to per minute) is 6.82%.

The subject of this question is determining the percent uncertainty of measurements. Percent uncertainty is calculated by dividing the uncertainty by the measurement and multiplying by 100%.

1. For the measuring tape, the uncertainty is 0.49 cm which first needs to be converted to meters (0.0049 m) since the measurement is given in meters. The percent uncertainty of the measuring tape is therefore (0.0049 m / 23m) * 100% = 0.0213%, a small percentage reflecting a high level of accuracy.

2. For counting heartbeats, the uncertainty is 3 beats and the measurement is 44 beats. Since it's measured in 30 seconds, we should double it to get beats per minute. Therefore, the uncertainty becomes 6 beats and the measurement becomes 88 beats. The percent uncertainty is therefore (6 beats / 88 beats) * 100% = 6.82%, a more considerable uncertainty.

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Answer:

[tex]\frac{(2m+3n)}{5mn}=\frac{2}{5n}+\frac{3}{5m}[/tex] is a rational number for any m and n; nonzero integers.

Step-by-step explanation:

We have been given that 'm' and 'n' are nonzero integers. We are asked to show that [tex]\frac{(2m+3n)}{5mn}[/tex] is a rational number.

We can rewrite our given number as:

[tex]\frac{2m}{5mn}+\frac{3n}{5mn}[/tex]

Cancelling out common terms:

[tex]\frac{2}{5n}+\frac{3}{5m}[/tex]

Since 'm' and 'n' are nonzero integers, so each part will be a rational number.

We know that sum of two rational numbers is always rational, therefore, our given number is a rational number.

Answer:

11/4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

12x+3−1=35

12x+3+−1=35

(12x)+(3+−1)=35(Combine Like Terms)

12x+2=35

12x+2=35

Step 2: Subtract 2 from both sides.

12x+2−2=35−2

12x=33

Step 3: Divide both sides by 12.

12x / 12 = 33 / 12x =

11 / 4

Answer:

Solution for the linear system:

a)  [tex]X_1=3, X_2=1, X_3=2[/tex]

b) [tex]x= w-1\\y=2z[/tex]

z and w are free, meaning that can have any value, for this reason, this system has infinite solutions.

Step-by-step explanation:

Gaussian-Jordan elimination consists of taking an augmented matrix, and transform it into its Row echelon form by means of row operation.  For notation, R_i will be the transform column, and r_i the actual one.

Linear System a)

First, you have to convert the system into matrix notation, in this case, column 1 corresponds to variable x_1, column 2 to x_2, column 3 to x_3 and column 4 to the system constants:

[tex]\left[\begin{array}{cccc}1&1&2&8\\-1&-2&3&1\\3&-7&4&10\end{array}\right][/tex]

Operations:

[tex]R_2=r_1+r_2\\R_3=-3r_1+r_3[/tex]

[tex]\left[\begin{array}{cccc}1&1&2&8\\0&-1&5&9\\0&-10&-2&-14\end{array}\right][/tex]

Operations:

[tex]R_2=-r_2[/tex]

[tex]\left[\begin{array}{cccc}1&1&2&8\\0&1&-5&-9\\0&-10&-2&-14\end{array}\right][/tex]

Operations:

[tex]R_3=10r_2+r_3[/tex]

[tex]\left[\begin{array}{cccc}1&1&2&8\\0&1&-5&-9\\0&0&-52&-104\end{array}\right][/tex]

Operations:

[tex]R_3=-\frac{1}{52}r_3[/tex]

[tex]\left[\begin{array}{cccc}1&1&2&8\\0&1&-5&-9\\0&0&1&2\end{array}\right][/tex]

[tex]x_1+x_2+2x_3=8\\x_2-5x_3=-9\\x_3=2[/tex]

[tex]x_3=2\\x_2=-9+5*2=1\\x_1=8-1-4=3[/tex]

Linear System b)

For this system, the process is the same as the above.  

Convert the system into matrix form

[tex]\left[\begin{array}{ccccc}1&-1&2&-1&-1\\2&1&-2&-2&-2\\-1&2&-4&1&1\\3&0&0&-3&-3\end{array}\right][/tex]

Operations:

[tex]R_2=-2r_1+r_2\\R_3=r_1+r_3\\R_4=-3r_1+r_4[/tex]

[tex]\left[\begin{array}{ccccc}1&-1&2&-1&-1\\0&3&-6&0&0\\0&1&-2&0&0\\0&3&-6&0&0\end{array}\right][/tex]

Operations:

[tex]R_2=\frac{1}{3}r_2[/tex]

[tex]\left[\begin{array}{ccccc}1&-1&2&-1&-1\\0&1&-2&0&0\\0&1&-2&0&0\\0&3&-6&0&0\end{array}\right][/tex]

Operations:

[tex]R_3=-r_2+r_3\\R_4=-3r_2+r_4[/tex]

[tex]\left[\begin{array}{ccccc}1&-1&2&-1&-1\\0&1&-2&0&0\\0&0&0&0&0\\0&0&0&0&0\end{array}\right][/tex]

Now you can write the system as equations:

[tex]x-y+2z-w=-1\\y-2z=0[/tex]

For w and z there is no unique answer, so the system result is expressed in terms of those variables. This system has infinite solutions.

Solution:

[tex]x= w-1\\y=2z[/tex]

z and w are free values.

Answer:

a) 1 unit per hour will be infused.

b) 5mL per hour will be infused.

Step-by-step explanation:

Each question can be solved as a rule of three with direct measures, that means we have a cross multiplication.

a. How many units per hour will be infused?

20 units are going to be infused in 20 hours. How many units are going to be infused each hour?

1 hour - x units

20 hours - 20 units

[tex]20x = 20[/tex]

[tex]x = \frac{20}{20}[/tex]

[tex]x = 1[/tex]

1 unit per hour will be infused.

b. How many milliliters per hour will be infused?

100mL are going to be infused in 20 hours. How many mL are going to be infused each hour?

1 hour - x mL

20 hours - 100 mL

[tex]20x = 100[/tex]

[tex]x = \frac{100}{20}[/tex]

[tex]x = 5[/tex]

5mL per hour will be infused.

Answer:

The 10th term of given sequence  is [tex]\frac{5}{32768}[/tex].

Step-by-step explanation:

The given sequence is

[tex]40,10, \frac{5}{2}, \frac{5}{8}, ....[/tex]

The given sequence is a geometric​ sequence because it have common ratio.

[tex]r=\frac{10}{40}=\frac{\frac{5}{2}}{10}=\frac{\frac{5}{8}}{\frac{5}{2}}=\frac{1}{4}[/tex]

In the given sequence the first term of the sequence is 40.

[tex]a_1=40[/tex]

The nth term of a GP is

[tex]a_n=a_1r^{n-1}[/tex]

where, [tex]a_1[/tex] is first term and r is common ratio.

Substitute [tex]a_1=40[/tex] and [tex]r=\frac{1}{4}[/tex] in the above formula.

[tex]a_n=40(\frac{1}{4})^{n-1}[/tex]

Substitute n=10 , to find the 10th term.

[tex]a_{10}=40(\frac{1}{4})^{10-1}[/tex]

[tex]a_{10}=\frac{5}{32768}[/tex]

Therefore the 10th term of given sequence  is [tex]\frac{5}{32768}[/tex].

Answer:

This was an observational study.

Step-by-step explanation:

Given is that parents of children completed a questionnaire on the child’s light exposure both at present and before the age of 2 years.

This was an observational study since there is no treatment or control group.

We know that treatment, control groups or treatment groups are not specific to randomized control experiments.

The study where parents of pediatric ophthalmology patients completed questionnaires about light exposure is an observational study because data were collected without manipulating any variables.

The study described in which parents filled out questionnaires about their children's light exposure is an example of an observational study, not a controlled experiment. In an observational study, researchers collect data without manipulating any variables. In this case, the researchers gathered information on light exposure by asking parents to complete a questionnaire, but they did not control or alter the children's light exposure themselves.

Unlike in an observational study, a controlled experiment involves actively manipulating one variable (the independent variable) to determine if it causes a change in another variable (the dependent variable), often comparing against a control group in a systematic way. An example of a controlled experiment includes the trial of Jonas Salk's polio vaccine, in which one group received the vaccine and another group received a placebo.

Answer:

a) [tex]y(t) = y_{0}e^{4t} + 2[/tex]. It does not have a steady state

b) [tex]y(t) = y_{0}e^{-4t} + 2[/tex]. It has a steady state.

Step-by-step explanation:

a) [tex]y' -4y = -8[/tex]

The first step is finding [tex]y_{n}(t)[/tex]. So:

[tex]y' - 4y = 0[/tex]

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

[tex]r - 4 = 0[/tex]

[tex]r = 4[/tex]

So:

[tex]y_{n}(t) = y_{0}e^{4t}[/tex]

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

[tex]y_{p}(t) = C[/tex]

So

[tex](y_{p})' -4(y_{p}) = -8[/tex]

[tex](C)' - 4C = -8[/tex]

C is a constant, so (C)' = 0.

[tex]-4C = -8[/tex]

[tex]4C = 8[/tex]

[tex]C = 2[/tex]

The solution in the form is

[tex]y(t) = y_{n}(t) + y_{p}(t)[/tex]

[tex]y(t) = y_{0}e^{4t} + 2[/tex]

b) [tex]y' +4y = 8[/tex]

The first step is finding [tex]y_{n}(t)[/tex]. So:

[tex]y' + 4y = 0[/tex]

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

[tex]r + 4 = [/tex]

[tex]r = -4[/tex]

So:

[tex]y_{n}(t) = y_{0}e^{-4t}[/tex]

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

[tex]y_{p}(t) = C[/tex]

So

[tex](y_{p})' +4(y_{p}) = 8[/tex]

[tex](C)' + 4C = 8[/tex]

C is a constant, so (C)' = 0.

[tex]4C = 8[/tex]

[tex]C = 2[/tex]

The solution in the form is

[tex]y(t) = y_{n}(t) + y_{p}(t)[/tex]

[tex]y(t) = y_{0}e^{-4t} + 2[/tex]

Answer:

Alice's weight is 100 lbs.

Step-by-step explanation:

Let's denote Jane's weight by J, and Alice's weight by A.

The exercise says that Jane is 20 lbs heavier than Alice. So that if you add 20 lbs to Alice's weight, you get Jane's weight. In equation form:

[tex]20+A=J[/tex]

It also mentions that Jane's weight is 120% that of Alice. So that if you multiply Alice's weight by 1.2, you get Jane's weight. In equation form:

[tex]1.2 \cdot A=J[/tex]

Plugging this second equation onto the first equation, we get:

[tex]20+A=1.2A[/tex]

And now solving for A:

[tex]20=1.2A-A[/tex]

[tex]20=0.2A[/tex]

[tex]\frac{20}{0.2}=A[/tex]

[tex]100=A[/tex]

Therefore Alice's weight is 100 lbs.

Answer:

There are two unknow values, your 8% which is the decrease and the main value which is "the sales last year".

It is correct, the number you gave as an answer $9798,91. Let's get the explanation by a rule of three.

Step-by-step explanation:

The 100 % was "the sales last year", the 8% are what the sales decreased but you don't have that number, you have the result in the substraction, $9015. So this are the step by step, hope you understand!

Answer:

The absolute and relative error of 355/113 compared with π is less than when π is compared with 22/7, that's why 355/113 is a better approximation for the actual value of π.

Step-by-step explanation:

The absolute error is the difference between a value measured and the real value.  

abs = π - approximation of π

The relative error indicates how large the absolute error is when compared with the actual value of π.

Now, let's calculate the absolute an relative error for each approximation of π, for simplicity the calculations will be rounded to 4 decimal digits.

rel = abs / π

abs = π - 22/7

abs = -0.0013

rel = (π - 22/7) / π

rel = -0.0402 %

abs = π - 355/113

abs = -2.6676 x10-7

rel =  (π - 355/113) / π

rel = -8.4914 x10-6 %

You can see that both the value of the absolute and relative error for the 355/113 approximation are smaller numbers, in conclusion, 355/113 is a better approximation for π.

Answer:

The negation will be : The shirt I am wearing to my interview is not orange.

Step-by-step explanation:

The negation of the statement means adding not, or nor to the statement.

The given statement is :

The shirt I’m wearing to my interview is orange.

The negation will be : The shirt I am wearing to my interview is not orange.